Optical information recording medium based on interference of converging spherical waves

ABSTRACT

An improved light-readable information recording medium is provided that comprises an optical data storage structure having lands and pits, in which the depth of the pits is about: 
                 λ     2   ⁢   n       ⁢     m     1   +     M   T   2           ,         
wherein λ is the wavelength of light used to read the information recording medium, m is the order of interference selected from a group consisting of odd integers, M T  is the transverse magnification, and n is the refractive index encountered by the reading light inside the pits. The invention also provides an improved optical reading system with the parameters satisfying the relationship:
 
               nd   =       λ     2   ⁢   n       ⁢     m     1   +     M   T   2             ,         
wherein λ is the wavelength of light used to read the information recording medium, m is the order of interference selected from a group consisting of odd integers, M T  is the transverse magnification, n is the refractive index encountered by the reading light inside the pits, and d is the depth of the pits.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of co-pending U.S. patent applicationNo. 11/338,000, filed Jan. 23, 2006, which is a continuation of U.S.patent application No. 10/202,983, filed Jul. 24, 2002, which is acontinuation-in-part of U.S. application No. 09/843,343, filed on Apr.25, 2001, now U.S. Pat. No. 6,771,585, which claims the benefit of U.S.Provisional Application No. 60/201,562, filed on May 1, 2000. The entiredisclosures of these applications are hereby incorporated by referenceherein in their entireties.

BACKGROUND OF THE INVENTION

This invention relates to an improved design of information recordingmedia, for example in the form of light-readable discs, and an improveddesign of optical reading equipment used for reading such informationrecording media. These improved designs, among other advantages, willallow greater tolerances in manufacturing of the information recordingmedia and will permit the use of less expensive optical readingequipment.

Information recording media in the form of light-readable discs are wellknown, as shown, for example in Kramer U.S. Pat. No. 5,068,846 and MeccaU.S. Pat. No. 5,995,481. Commercially available audio compact discs(“CDs”) and compact disc read-only memories (“CD-ROMs”) are examples ofrecording media of this general type.

The predominant portion of a typical light-readable disc comprises atransparent material, such as polycarbonate plastic. Information in theform of binary data is contained in a pit and land structure impressedalong the top surface of this transparent material. The structure iscovered by a very thin metal reflective layer, typically aluminum. Aprotective layer, typically lacquer, is then placed over the reflectivelayer, so that the protective layer fills the indentations in thereflective layer and provides a smooth, substantially planar uppersurface for the disc on which a label or other information may beplaced.

The pits and lands optical structure of the light-readable discs mediumcan be read by a laser beam focused on the reflective layer. The laserbeam passes through the bottom of the transparent material and throughthe optical structure of pits and lands (which is seen by the laser frombelow as a series of bumps and lands), and is reflected off thereflective layer, through the transparent material and out of the mediumto an optical reading structure.

Several publications conclude, based on elementary properties ofinterference between the incident and reflected waves, that the maximumextinction of the returned light is obtained when the light reflected bya pit is in antiphase with the light reflected by the surrounding land,namely, when the pit depth/bump height (depending on the plane ofreference) is a quarter-wavelength. (G. Bouwhuis et al., Principles ofOptical Disc System, 1^(st) ed.(1985); K. Pohlmann, The Compact Disc,Updated ed. (1992); Dil et al., J. Opt. Soc. Am., 69: 950 (1979)). Thishas led to the standardization of pit depth/bump height (depending uponthe plane of reference) in commercial light-readable informationrecording media at just less than approximately one-quarter of thewavelength of the laser light within the transparent material.

However, recent findings revealed that the quarter wavelength criteriondid not predict optimum results under all circumstances. As reported inMecca U.S. Pat. No. 5,995,481, it had been determined that an improvedlight-readable recording disc was achieved by designing the pitdepth/bump height to be approximately one-half of the wavelength of thelaser light source. Not only such a disc had been found to be operable,but it had been determined that the intensity difference between thebump and land areas detected by an optical reader was actually greaterthan for the one-quarter wavelength pit previously thought to beoptimal.

Numerous efforts had been undertaken to understand and/or explain theunexpected and improved results obtained by controlling pit height toapproximately one-half the wavelength of light. None have borne fruituntil now.

The present invention provides a way to optimize performance of bothinformation recording media and the optical reading equipment by using atwo-point-source model to simulate the waves reflected from the datasurface of the recording media. The improved results promise substantialsavings in the design and manufacture of less sensitive and less costlylight-reading systems, as well as in disc manufacturing. Since a higherintensity signal difference is generated, manufacturing tolerances canbe relaxed without sacrificing quality in the output and reading ofdata, leading to higher yields and lower costs.

In view of the foregoing, it is an object of this invention to provide alight-readable information recording medium and an optical reader thatgenerate greater signal intensity difference, which can improve thequality of reproduction, reduce the cost and complication of opticalreading devices, and provide for greater tolerance in the manufacturingof such recording media.

SUMMARY OF THE INVENTION

These and other objects of the present invention are accomplished asfollows. According to the new model, two spherical (not plane) wavesreturn from the data surface and travel to the objective lens. Onespherical wave is due to the reflection of the read-out beam from thepit, the other is due to the reflection from the surrounding land. Thereturning field then results from the superposition of two sphericalwaves, which first diverge from the disc and are then focused by theobjective lens onto the photodetector. Consequently, according to themodel presented in this invention, one is dealing with interference oftwo converging spherical waves with slightly different foci, slightlydifferent focal lengths and slightly different cone angles, rather thanwith interference of two plane waves. The focal regions of the twoconverging spherical waves are overlapping and the interference of thetwo focused spherical waves takes place in the common region.

This two-point-source model was next applied to investigate how binarydata recorded on a surface of an information recording medium aretransferred into series of light pulses. The analysis resulted in anexpression for the optical pit depth in terms of the system parametersfor which destructive interference leads to a maximum extinction of thelight in the focal region:

${\Delta_{opt} = {\frac{\lambda}{2}\frac{m}{1 + M_{T}^{2}}}},$wherein λ is the wavelength of the light used to read the informationrecording medium, m is the order of interference selected from a groupconsisting of odd integers, and M_(T) is the transverse magnification ofthe reader.

Accordingly, the present invention provides an information recordingmedium, which can be read by an optical reader using reflected light,comprising an optical data storage structure including pits and lands,in which the depth of the pits is equal to about:

${\frac{\lambda}{2n}\frac{m}{1 + M_{T}^{2}}},$wherein λ is the wavelength of the light used to read the informationrecording medium, m is the order of interference selected from a groupconsisting of odd integers, n is the refractive index of the mediaencountered by the reading light inside the pits, and M_(T) is thetransverse magnification of the optical reader.

In addition, the invention facilitates building a system for opticallyreading stored information, which comprises an information recordingmedium having a light-reflecting surface formed as a data storagestructure including pits and lands, a light source directed at the datastorage structure so that the light is reflected in accordance with theinformation recorded using pits and lands, and an optical reader fordetection of the reflected light and reading of the information recordedby means of pits and lands. According to the principles of theinvention, the wavelength λ of the light used to read the informationrecording medium, the interference order m selected from a groupconsisting of odd integers, the transverse magnification M_(T) of theoptical reader, the refractive index n of the media within the pits, andthe depth of the pits d satisfy the following relationship:

${nd} = {\frac{\lambda}{2}{\frac{m}{1 + M_{T}^{2}}.}}$

Further features of the invention, its nature and various advantageswill be more apparent from the accompanying drawings and the followingdetailed description of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1 a and 1 b represent a two-point-source model of lightinteraction with a pits and lands structure: Two monochromatic pointsources S₁ and S₂, generating light of the same wavelength λ, arelocated on the axis of the objective lens. The point source S₁ isassociated with reflection of the light from the land. The point sourceS₂ is associated with the reflection of the light from the pit. Δdenotes the pit depth. FIG. 1 a shows the notation used. FIG. 1 b showstwo wavefronts W₁ and W₂ of radii R′₁ and R′₂, centered at the pointsS′₁ and S′₂ respectively and passing through the center O of a circularaperture of radius α.

FIG. 2 represents isophotes (lines of equal intensity) in the focalregion. The tubular structure of the central portion should be noted(Adapted from E. H. Linfoot and E. Wolf, Proc. Phys. Soc., B, 69 (1956),823).

FIG. 3 shows a plot of optimum pit depth Δ_(opt) as a function of thetransverse magnification M_(T) of the system, when m=1, 3 and 5.

FIG. 4 shows a plot of the order of interference m as a function of thetransverse magnification M_(T) of the system, when the optimum pit depthΔ_(opt) has the values λ/2 and λ/4.

FIG. 5 is a simplified view of a light-readable information recordingdisc, providing an enlarged view of one-path of optically recordedinformation.

FIG. 6 is a cross-sectional view of this light-readable informationrecording disc, shown along the path of the recorded information.

FIG. 7 shows contour lines of equal contrast C of the detector signal asa function of the pit depth and of the transverse magnification of thesystem.

FIG. 8 shows contour lines of equal contrast C as a function of pitdepth and of the order of interference m.

FIG. 9 shows the contrast C of receiving signal plotted as a function ofΔ/λ, when the transverse magnification M_(T)=2, M_(T)=1 and M_(T)<<1,showing that C varies between the values 1 and 0.

DETAILED DESCRIPTION OF THE INVENTION

The objects of the invention are accomplished by considering a modeldescribing the interaction of two converging spherical waves in thefocal region of an optical reading system, applying this model toinvestigate how the binary data recorded on a light-readable informationrecording medium's surface are transferred into a series of lightpulses, and deriving the relationship that must govern the parameters ofa light-readable information recording medium and the system used toread it, so that destructive interference leads to a maximum extinctionof light in the focal region.

I. Imaging of Two Point Sources

Consider two point sources S₁ and S₂ of light of the same wavelength λ,which are placed close to each other on the axis of a thin lens of focallength f, which fills an aperture of radius α as shown in FIG. 1 a. LetΔ=R ₁ −R ₂  (1)be the separation of points S₁ and S₂, with R₁ and R₂ being the radii ofcurvature of the two spherical wavefronts immediately behind the thinlens. On the other side of the lens, two spherical wavefronts emerge,converging to points S₁′ and S₂′. We denote their radii of curvature byR₁′ and R₂′, respectively. For the point source S₁, the radii ofcurvature R₁ and R₁′ satisfy the lens relation:

$\begin{matrix}{{{\frac{1}{R_{1}} + \frac{1}{R_{1}^{\prime}}} = \frac{1}{f}},} & (2)\end{matrix}$and for the point source S₂, the radii of curvature R₂ and R₂′ satisfy asimilar relation:

$\begin{matrix}{{\frac{1}{R_{2}} + \frac{1}{R_{2}^{\prime}}} = {\frac{1}{f}.}} & (3)\end{matrix}$The separation of the image points S₁′ and S₂′ is given by (see FIG. 1a):Δ′=R ₁ ′−R ₂ ′=−M _(T) ²×Δ,  (4)where M_(T) is the transverse magnification of the system. Here we haveassumed that the two spherical wave systems have the same transversemagnification.II. Diffraction Integrals

As we have indicated, we consider two spherical waves, say V₁ ^((t)) andV₂ ^((t)), generated by the two point sources S₁ and S₂, emerging fromthe aperture. At typical points Q₁ and Q₂ on the wavefronts (see FIG. 1b) that pass through the center O of the aperture, the fielddistributions can be expressed in the form:

$\begin{matrix}{{{V_{1}^{(t)}\left( {Q_{1},t} \right)} = {A\frac{{\mathbb{e}}^{{- {\mathbb{i}}}\;{kR}_{1}^{\prime}}}{R_{1}^{\prime}}{\mathbb{e}}^{{- {\mathbb{i}\omega}}\; t}}},{{V_{2}^{(t)}\left( {Q_{2},t} \right)} = {A\frac{{\mathbb{e}}^{- {{\mathbb{i}}{({{kR}_{2}^{\prime} + \theta_{0}})}}}}{R_{1}^{\prime}}{\mathbb{e}}^{{- {\mathbb{i}\omega}}\; t}}},} & {\left( {5a} \right),\left( {5b} \right)}\end{matrix}$where A is a constant amplitude, t denotes the time andθ₀=kΔ  (6)is the phase shift introduced by the spatial separation Δ of the twopoint sources S₁ and S₂.

According to the Huygens-Fresnel principle (M. Born & E. Wolf,Principles of Optics, 7^(th) ed. (1999), sec. 8.2), the diffractedfields at a point P of the detector plane (see FIG. 1 b) are given bythe expressions (with time-periodic factor exp(−iωt) omitted):

$\begin{matrix}{{{U_{1}(P)} = {{- \frac{\mathbb{i}}{\lambda}}\frac{A\;{\mathbb{e}}^{{- {\mathbb{i}}}\;{kR}_{1}^{\prime}}}{R_{1}^{\prime}}{\int_{W_{1}}{\int\ {\frac{{\mathbb{e}}^{{\mathbb{i}}\;{kz}_{1}}}{s_{1}}{\mathbb{d}S}}}}}},{and}} & \left( {7a} \right) \\{{{U_{2}(P)} = {{- \frac{\mathbb{i}}{\lambda}}\frac{A\;{\mathbb{e}}^{- {{\mathbb{i}}{({{kR}_{2}^{\prime} + \theta_{0}})}}}}{R_{2}^{\prime}}{\int_{W_{2}}{\int\ {\frac{{\mathbb{e}}^{{\mathbb{i}}\;{kz}_{2}}}{s_{2}}{\mathbb{d}S}}}}}},} & \left( {7b} \right)\end{matrix}$where s₁ and s₂ denote the distances Q₁P and Q₂P and the integralsextend over the wavefronts W₁ and W₂ filling the aperture.

Let (z₁, r₁, ψ₁) and (z₂, r₂, ψ₂) be the two sets of coordinates of thepoint P in the focal regions of the two converging spherical wavesoriginating from the point sources S₁ and S₂. The origins of the twocoordinate systems are at S₁′ and S₂′, namely, at the image points ofthe point sources S₁ and S₂. The z-coordinates of the two focusingsystems have a separationz ₁ =z ₂+Δ′,  (8)along the common direction OS₁′ and OS₂′ (see FIG. 1 a). The radialdistances from the z-axes are:r₁=r₂=r  (9)and the azimuthal angles are also equal, i.e., ψ₁₋ψ₂₋ψ.

It is convenient to introduce the Lommel parameters (u₁, ν₁) and (u₂,ν₂) which, together with the angle ψ specify the position of the fieldpoint P:

$\begin{matrix}{{u_{1} = {\left( \frac{a}{R_{1}^{\prime}} \right)^{2}{kz}_{1}}},{{v_{1} = {\left( \frac{a}{R_{1}^{\prime}} \right){kr}_{1}}};}} & {\left( {10a} \right),\left( {10b} \right)} \\{{u_{2} = {\left( \frac{a}{R_{2}^{\prime}} \right)^{2}{kz}_{2}}},{v_{2} = {\left( \frac{a}{R_{2}^{\prime}} \right){{kr}_{2}.}}}} & {\left( {11a} \right),\left( {11b} \right)}\end{matrix}$Because the fields are rotationally symmetric about the z-axis, thediffracted fields are independent of the azimuthal angle ψ.

The photodetector, which changes the intensity variations of the lightinto an electrical signal, is assumed to be placed at the point z₁=z₀ inthe focal regions of the two converging spherical waves. We thenobtained from Eqs. (10) and (11) the following expressions for theLommel parameters in the detector plane:

$\begin{matrix}{{u_{1} = {\left( \frac{a}{R_{1}^{\prime}} \right)^{2}{kz}_{0}}},{{v_{1} = {\left( \frac{a}{R_{1}^{\prime}} \right){kr}_{1}}};}} & {\left( {12a} \right),\left( {12b} \right)} \\{{u_{2} = {\left( \frac{a}{R_{2}^{\prime}} \right)^{2}{k\left( {\Delta^{\prime} + z_{0}} \right)}}},{v_{2} = {{\left( \frac{a}{R_{2}^{\prime}} \right){kr}_{2}} = {\left( \frac{R_{1}^{\prime}}{R_{2}^{\prime}} \right){v_{1}.}}}}} & {\left( {13a} \right),\left( {13b} \right)}\end{matrix}$

Assuming, as is usually the case, that the focusing system of focallength f has a high numerical aperture, the field in the region of thegeometrical focus may be expressed in the form (Born & Wolf, sec. 8.8):

$\begin{matrix}{{{U(P)} = {{- \frac{2\pi\;{\mathbb{i}}\; a^{2}\mspace{14mu} A}{\lambda\; f^{2}}}{\mathbb{e}}^{{{\mathbb{i}}{(\frac{f}{a})}}^{2}u}{\int_{0}^{1}{{J_{0}({\nu\rho})}{\mathbb{e}}^{{- \frac{1}{2}}{\mathbb{i}}\; u\;\rho^{2}}\ \rho{\mathbb{d}\rho}}}}},} & (14)\end{matrix}$where J₀ is the Bessel function of the first kind and zero order. We nowapply Eq. (14) to the two converging spherical waves discus in Sec. Iabove.

On substituting u=u₁, ν=ν₁ and f=R₁′ into Eq. (13), we obtain for thediffracted field of the first converging spherical wave the expression:

$\begin{matrix}{{U_{1}(P)} = {{- \frac{2\pi\;{\mathbb{i}}\; a^{2}\mspace{14mu} A}{{\lambda\left( R_{1}^{\prime} \right)}^{2}}}{\mathbb{e}}^{{{\mathbb{i}}{(\frac{R_{1}^{\prime}}{a})}}^{2}u_{1}}{\int_{0}^{1}{{J_{0}\left( {\nu_{1}\rho} \right)}{\mathbb{e}}^{{- \frac{1}{2}}{\mathbb{i}}\; u_{1}\rho^{2}}\ \rho{{\mathbb{d}\rho}.}}}}} & (15)\end{matrix}$

Similarly, on substituting u=u₂, ν=ν₂ and f=R₂′ into Eq. (13), we obtainthe following expression of the diffracted field for the secondconverging spherical wave:

$\begin{matrix}{{U_{2}(P)} = {{- \frac{2\pi\;{\mathbb{i}}\; a^{2}\mspace{14mu} A}{{\lambda\left( R_{2}^{\prime} \right)}^{2}}}{\mathbb{e}}^{{{\mathbb{i}}{(\frac{R_{2}^{\prime}}{a})}}^{2}u_{2}}{\int_{0}^{1}{{J_{0}\left( {\nu_{2}\rho} \right)}{\mathbb{e}}^{{- \frac{1}{2}}{\mathbb{i}}\; u_{2}\rho^{2}}\ \rho{{\mathbb{d}\rho}.}}}}} & (16)\end{matrix}$The subscripts 1 and 2 affixed to the symbol U(P) for the diffractedfields indicate that they originated from the point sources S₁ and S₂,respectively.

The field distribution in the focal region arising from the suppositionof the two fields given by Eqs. (15) and (16) can be expressed as:

$\begin{matrix}\begin{matrix}{{U(P)} = {{{U_{1}(P)} + {U_{2}(P)}} =}} \\{= {{- \frac{2\pi\;{\mathbb{i}}\; a^{2}\mspace{14mu} A}{{\lambda\left( R_{1}^{\prime} \right)}^{2}}}{\left\{ {{{\mathbb{e}}^{{{\mathbb{i}}{(\frac{R_{1}^{\prime}}{a})}}^{2}u_{1}}{\int_{0}^{1}{{J_{0}\left( {\nu_{1}\rho} \right)}{\mathbb{e}}^{{- \frac{1}{2}}{\mathbb{i}}\; u_{1}\rho^{2}}\ \rho{\mathbb{d}\rho}}}} + {{{\mathbb{e}}^{{\mathbb{i}}{\lbrack{{(\frac{R_{2}^{\prime}}{a})}^{2}u_{2}{–\theta}_{0}}\rbrack}}\left( \frac{R_{1}^{\prime}}{R_{2}^{\prime}} \right)}^{2}{\int_{0}^{1}{{J_{0}\left( {\nu_{2}\rho} \right)}{\mathbb{e}}^{{- \frac{1}{2}}{\mathbb{i}}\; u_{2}\rho^{2}}\rho\ {\mathbb{d}\rho}}}}} \right\}.}}}\end{matrix} & (17)\end{matrix}$According to Eq. (17), the intensity distribution I(P)=|U(P)|² in thefocal region is, therefore,

$\begin{matrix}{{{I(P)} = \left| {2\left\{ {{\sqrt{I_{02}}{\mathbb{e}}^{{{\mathbb{i}}{(\frac{R_{2}^{\prime}}{a})}}^{2}u_{1}}{\int_{0}^{1}{{J_{0}\left( {\nu_{1}\rho} \right)}{\mathbb{e}}^{{- \frac{1}{2}}{\mathbb{i}}\mspace{11mu}{u\;}_{1}\rho^{2}}\ \rho{\mathbb{d}\rho}}}} + {\sqrt{I_{02}}{\mathbb{e}}^{{\mathbb{i}}{\lbrack{{{(\frac{R_{2}^{\prime}}{a})}^{2}u_{2}} - \theta_{0}}\rbrack}}{\int_{0}^{1}{{J_{0}\left( {\nu_{2}\rho} \right)}{\mathbb{e}}^{{- \frac{1}{2}}{\mathbb{i}}\mspace{11mu} u_{2}\rho^{2}}\ \rho{\mathbb{d}\rho}}}}} \right\}} \right|^{2}},\mspace{79mu}{where}} & (18) \\{\mspace{79mu}{I_{01} = {{{\left( \frac{\left. {\pi\; a^{2}} \middle| A \right|}{{\lambda\left( {\, R_{1}^{\prime}} \right)}^{2}} \right)\;}^{2}\mspace{11mu}{and}\mspace{14mu} I_{02}} = \left( \frac{\left. {\pi\; a^{2}} \middle| A \right|}{\lambda\;\left( R_{2}^{\prime} \right)^{2}} \right)^{2}}}} & (19)\end{matrix}$are constants.III. The Validity of Eq. (17) in the Overlapping Focal Regions

Equation (17) is valid under the condition that the focal regions of twoconverging spherical waves overlap. Let us examine this situation.

The three-dimensional light-distribution near the focus can berepresented by isophotes, namely by contour lines of equal intensity(see FIG. 2 or FIG. 8.41 of Born & Wolf). Important for ourconsideration is the tubular structure in the blight central portion ofthe figure, which indicates the focal depth. The focal depths of thefocused fields originated from the point sources S₁ and S₂ are of theorder of (Born & Wolf, Eq. (27) in sec. 8.8):

$\begin{matrix}{{\text{|}\Delta\; z_{1}\text{|}} = {{\frac{\lambda}{2}\left( \frac{R_{1}^{\prime}}{a} \right)^{2}\mspace{14mu}{and}\mspace{14mu}\text{|}\Delta\; z_{2}\text{|}} = {\frac{\lambda}{2}{\left( \frac{R_{2}^{\prime}}{a} \right)^{2}.}}}} & {\left( {20a} \right),\left( {20b} \right)}\end{matrix}$Hence Eq. (17) will be a good approximation provided that:|Δ′|≦|Δz ₁| and |Δ′|≦|Δz ₂|.  (21a), (21b)On substituting for Eqs. (4), (20a) and (20b) into Eqs. (21a) and (21b),we obtain the following estates for the range of validity of our theory:

$\begin{matrix}{{M_{T}^{2} \times \Delta} \leq {\frac{\lambda}{2}\left( \frac{R_{1}^{\prime}}{a} \right)^{2}\mspace{14mu}{and}\mspace{14mu} M_{T}^{2} \times \Delta} \leq {\frac{\lambda}{2}{\left( \frac{R_{2}^{\prime}}{a} \right)^{2}.}}} & {\left( {22a} \right),\left( {22b} \right)}\end{matrix}$With the choice Δ=λ/2 and M_(T)≈(R₁′/R₁)≈(R₂′/R₂), Eqs. (22a) and (22b)become:α≦R₁ and α≦R₂  (23a),(23b)The numerical aperture of commonly used objective lens lies in the rangebetween about 0.43 to 0.5, i.e., R₁ and R₂ are in the range between1.73α and 2.10α. Hence, the inequalities in Eqs. (23a) and (23b) aresatisfied. We may, therefore, conclude that the tubular structures ofthe focal regions of two converging spherical waves overlap and Eq. (17)correctly describes the combined effects of the two waves in theoverlapping focal regions.IV. Interference Effects in the Focal Region

To obtain a better insight into the structure of the region ofsuperposition, we rewrite Eq. (18) in the form:I(P)=I ₁(P)+I ₂(P)+2√{square root over (I ₁(P)I ₂(P))}{square root over(I ₁(P)I ₂(P))} cos(φ₁−φ₂),  (24)where

$\begin{matrix}{{{I_{1}(P)} = \left. I_{01} \middle| {2{\int_{0}^{1}{{J_{0}\left( {\nu_{1}\rho} \right)}{\mathbb{e}}^{{- \frac{1}{2}}{\mathbb{i}}\; u_{2}\rho^{2}}\ \rho{\mathbb{d}\rho}}}} \right|^{2}},{and}} & \left( {25a} \right) \\{{{I_{2}(P)} = \left. I_{02} \middle| {2{\int_{0}^{1}{{J_{0}\left( {\nu_{2}\rho} \right)}{\mathbb{e}}^{{- \frac{1}{2}}{\mathbb{i}}\; u_{2}\rho^{2}}\ \rho{\mathbb{d}\rho}}}} \right|^{2}},} & \left( {25b} \right)\end{matrix}$are the intensity distributions in focal regions of the two convergingspherical waves that represent the waves returning from the pit and fromthe surrounding land on the data surface of a recording mediumrespectively. After a long calculation, the phase factors φ₁ and φ₂ canbe expressed in the form:

$\begin{matrix}{{\phi_{1} = {\left( \frac{R_{1}^{\prime}}{a} \right)^{2}u_{1}}},} & \left( {26a} \right) \\{\phi_{2} = {{\left( \frac{R_{2}^{\prime}}{a} \right)^{2}u_{2}} - {\theta_{0}.}}} & \left( {26b} \right)\end{matrix}$where θ₀, given by Eq. (6), represents the phase shift between the tworeturned waves. Let us suppose that the photodetector is located at thedistance:z ₀=−Δ′/2  (27)from the point S₁′. It then follows from Eqs. (12a) and (13a) that:

$\begin{matrix}{u_{1} = {{{- {k\left( \frac{a}{R_{1}^{\prime}} \right)}^{2}}\frac{\Delta^{\prime}}{2}\mspace{14mu}{and}\mspace{14mu} u_{2}} = {{- {k\left( \frac{a}{R_{2}^{\prime}} \right)}^{2}}{\frac{\Delta^{\prime}}{2}.}}}} & {\left( {28a} \right),\left( {28b} \right)}\end{matrix}$On substituting Eqs. (28a) and (28b) into Eqs. (26a) and Eq. (26b), weobtain for the phase difference φ₁−φ₂ the expression:

$\begin{matrix}{{\phi_{1} - \phi_{2}} = {{\left( \frac{R_{1}}{a} \right)^{2}u_{1}} - {\left( \frac{R_{2}}{a} \right)^{2}u_{2}} + {\theta_{0}.}}} & (29)\end{matrix}$Next, on substituting from Eqs. (4), (6), (28a) and (28b) into Eq. (29),we find that:φ₁−φ₂ =−kΔ′+kΔ=kΔ(1+M _(T) ²).  (30)

When the laser spot on the disc surface scans over a pit, the intensityin the overlapped region is given by the expression:I _(pit)(P)=I ₁(P)+I ₂(P)+2√{square root over (I ₁(P)I ₂(P))}{squareroot over (I ₁(P)I ₂(P))} cos [kΔ(1+M _(T) ²)].  (31)

On the other hand, when the laser spot scans over the land, the phasedifference φ₁−φ₂=(m−1)π, (m=1, 3, 5 . . . ). The intensity in theoverlapped region is then a maximum and is given by the expression:I _(land)(P)=I ₁(P)+I ₂(P)+2√{square root over (I ₁(P)I ₂(P))}{squareroot over (I ₁(P)I ₂(P))}.  (32)

Intensity distribution in the focal region of a system of large angularaperture is symmetrical about the focal plane (see Born & Wolf, orCollett et al., Opt. Lett., 5: 264 (1980)). Therefore, from Eqs. (25a)and (25b):I ₁(−u ₁,ν₁)=I ₁(u ₁,ν₁) and I ₂(−u ₂,ν₂)=I ₂(u ₂,ν₂).  (33a), (33b)If we ignore the slight difference between R₁′ and R₂′, we findimmediately from Eqs. (28a) and (28b) thatu ₁ ≈−u ₂,  (34a)and from Eqs. (12b) and (13b) thatν₁≈ν₂.  (34b)We can therefore conclude thatI ₁(P)≈I ₂(P)  (34)The intensity distributions given by Eqs. (31) and (32) then reduce toI _(land)(P)=4I ₁(P)  (36a)andI _(pu)(P)≈4I ₁(P)cos² [kΔ(1+M _(T) ²)/2]  (36b)

It follows that the contrast C of the photodetector output signal isgiven by the expression:

$\begin{matrix}{C = {\frac{{I_{land}(P)} - {I_{pit}(P)}}{{I_{land}(P)} + {I_{pit}(P)}} \cong \frac{\sin^{2}\left\lbrack {k\;{{\Delta\left( {1 + M_{T}^{2}} \right)}/2}} \right\rbrack}{1 + {\cos^{2}\left\lbrack {k\;{{\Delta\left( {1 + M_{T}^{2}} \right)}/2}} \right\rbrack}}}} & (37)\end{matrix}$

FIG. 7 presents contour lines of equal contrast C of the detector signalas a function of the pit depth Δ and of the transverse magnificationM_(T). In FIG. 9, the contrast C of receiving signal is plotted as afunction of Δ/λ, when the transverse magnification M_(T)=2, M_(T)=1, andM_(T)<<1, showing that C varies between the values 1 and 0. When C=0,the contrast is zero, meaning that no signal returns from the disk. Thishappens whensin [kΔ(1+M _(T) ²)/2]=0,  (38)i.e., whenκΔ(1+M _(T) ²)=mπ(m=0, 2, 4 . . . ),  (39)resulting in the following expression for the pit depth:

$\begin{matrix}{\Delta = {\frac{\lambda}{2}\frac{m}{1 + M_{T}^{2}}\mspace{20mu}{\left( {{m = 0},2,{4\mspace{14mu}\ldots}}\mspace{14mu} \right).}}} & (40)\end{matrix}$

According to Equation (37), the maximum contrast C=1 is achieved whensin² [kΔ(1+M _(T) ²)/2]=1 and cos² [kΔ(1+M _(T) ²)/2]=0,  (41)i.e., whenkΔ(1+M _(T) ²)=mπ(m=1, 3, 5, . . . ),  (42)resulting in the following expression for the optimum depth of the pits:

$\begin{matrix}{{\Delta_{opt} = {\frac{\lambda}{2}\frac{m}{1 + M_{T}^{2}}}},\;{\left( {{m = 1},3,5,\mspace{11mu}\ldots}\mspace{14mu} \right).}} & (43)\end{matrix}$Equation (43) is the main result of our analysis. In FIG. 3 the optimumpit depth Δ_(opt) is plotted as a function of the transversemagnification M_(T) for the cases when m=1, 3 and 5. FIG. 8 presentscontour lines of equal contrast C as a function of pit depth Δ and ofthe order of interference m as defined in Equations (39) and (42).

It can be seen from Eq. (43) that the optimum depth Δ_(opt) of theinformation pits is a function of three parameters: the wavelength λ,the transverse magnification M_(T) of the system, and the order ofinterference m. For systems of large magnification (M_(T) ²>>1):

$\begin{matrix}{{\Delta_{opt} \approx {\frac{\lambda}{2}\left( \frac{m}{M_{T}^{2}} \right)\mspace{20mu}\left( {{m = 1},3,{5\mspace{14mu}\ldots}}\mspace{14mu} \right)}},} & (44)\end{matrix}$which indicates that m has the same order of magnitude as M_(T) ², ifthe pit depth is not much smaller than λ. A smaller m is preferable inorder to tolerate a greater error in the manufacturing process.

The equations in this text have been derived under the assumption thatthe disk is read in reflection from the airside. For commerciallyavailable systems, the disk is read in reflection from the substrateside. For plastic substrate with a refractive index n, Snell's law ofrefraction states that nsinΘ is a constant, the numerical aperture doesnot change at the transition of light from plastic substrate to air.Furthermore, the phase changes associated with the wavefront distortiondue to spherical aberration at the transition are assumed to have beencompensated by the aspherical objective. Under these circumstances, theimpact of the refraction is on the wavelength and on the cone angle,which are different on the two sides of the boundary. Taking all thesefactors into account, the optimum condition shown in Eq. (43) can berecessed by a simple modification of the wavelength, i.e.,

$\begin{matrix}{d = {\frac{\lambda_{n}}{2}\frac{m}{1 + M_{T}^{2}}\mspace{14mu}{\left( {{m = 1},3,5,\;\ldots}\mspace{14mu} \right).}}} & (45)\end{matrix}$where λ_(n)=λ/n is the wavelength in the substrate.

The foregoing analysis shows that the optimum pit depth is a function offour parameters: the wavelength λ, the magnification M_(T) of thesystem, the order of interference m, and the refractive index n.

FIG. 9 shows the dependence of the optimum depth Δ_(opt) on thetransverse magnification M_(T) of the system for the case when the orderof interference m=1. For a system of low magnification, namely, withM_(T)<<1 and for the lowest order of interference, Eq. (45) provides thefollowing expression for the optimum pit depth:

$\begin{matrix}{d = {\frac{\lambda_{n}}{2}.}} & (46)\end{matrix}$It is also seen from FIG. 9 that the system having low transversemagnification (M_(T)<<1) is not optimized when d=λ_(n)/4. The contrastthen has the value of 0.33. A disk with the pit depth equal to aquarter-wavelength is optimized only in systems with transversemagnification M_(T)≈1. On substituting the values M_(T)=1 and m=1 intoEq. (45), we see that

$\begin{matrix}{d = {\frac{\lambda_{n}}{4}.}} & (47)\end{matrix}$

We have thus shown that both the half-wavelength and thequarter-wavelength criteria can be derived from Eq. (45) under theconditions of different system magnifications. The optimum pit depth isnot a universal value, but a result of optimization of the whole systemwhen the laser of a certain wavelength is used.

Table 1 summarizes the optical characteristics of some commerciallyavailable systems.

TABLE 1 Optical characteristics of commercially available CD- andDVD-players. The refractive index of polycarbonate substrate n ≈ 1.57Wavelength Transverse in N.A. magnification Wavelength substrate Depthof pit Disk- Detector- of the system λ (nm) λ_(n) (nm) d (nm) d/λ_(n)side side M_(T) CD-player 780 497 100-120(*) 0.20-0.24 0.45 ≈0.10 ≈5DVD-player 650 414 100 0.24 0.60 ≈0.15 ≈5 (*)Depending on themanufacturer

The data in Table 1 indicate that the pit depths of commerciallyavailable CDs and DVDs lie approximately in the rangeλ/8≦d≦λ/6.  (48a)For plastic substrates with a refractive index of approximately 1.5, therange of the pit depths can be expressed asλ_(n)/5.3≦d≦λ _(n)/4.  (48b)which is close to the value of a quarter-wavelength.

For commercially available systems, we have found a unique transversemagnification M_(T)≈5 as shown in Table 1, which must be a designconsideration for compatibility of discs of different data storagedensities.

In conclusion, the pit depth of a compact disk has a profound effect onthe detector signal. In practice, the choice of the pit depth would be acompromise between the signal quality and the yield of injection moldingfor replication of the disc. Future systems will require higher storagedensities, which may need a reduction of pit width. As a consequence,the pit depth may be reduced proportionally to avoid the sharp edges ofthe pit that causes damage when the replica is moved from the mold. Inthis case, the pit depth becomes much smaller than a quarter wavelength,and only Eq. (45) can predict the optimum result.

The objects of the present invention are thus accomplished by providing,light-readable information recording media and optical systems forreading such information recording media with the relevant parameterssubstantially satisfying equation (43) or (45). The informationrecording medium can be a disc in which the optical structure is exposedto air, such that the laser light strikes a reflective surface directly.

It is of no importance to the invention whether pits or bumps areutilized along with lands in the optical storage structure, as thesestructures are equivalent for the purposes of this invention. As can beseen from equation (39), it is the optical distance between the bump/pitand the land that is of essence. Therefore, whenever this disclosurerefers to pits and their depth, these words should be interpreted torefer to bumps and their height as well. It is also implicit that thereflecting surface of a data storage structure comprising pits and landscan be only partially reflecting.

Embodiment 1

FIG. 5 depicts a light-readable information recording medium in theshape of a disc 1, as viewed from below. The figure also shows a greatlymagnified section of one path of optically recorded information 2, inwhich pits/bumps are designated as 4′ and 4″ and lands are designated as3, 3′ and 3″.

FIG. 6 depicts a cross-sectional view along the length of this magnifiedsection of optically recorded information 2. A transparent material 5,preferably polycarbonate (although materials such as polymethylmethacrylate and photo polymer can be used), forms the base of the disc1, with a substantially planar lower surface 6. The top surface of thetransparent material 5 is characterized by a series of lands 3, 3′ and3″, separated by pits 4 and 4′. A thin layer of reflective materialcovers the lands 3, 3′ and 3″ and the pits 4 and 4′ along the topsurface of the transparent material 5. Although more costly materials,such as gold or silver, would yield a longer life with betterreflectivity, aluminum is typically used as the reflective material 7. Aprotective layer 8, preferably lacquer, is placed atop the reflectivematerial. The protective layer 8 is deposited unevenly so as to providea substantially planar top surface 9 of the light-readable informationrecording disc 1. A label or other information may be placed upon thistop surface 9.

Although the exact size and dimensions of the light-readable informationrecording disc 1 are matters of choice, the most common disc incommercial use today is 120 millimeters in diameter aid 1.2 millimetersthick. The layer of reflective material 7 is preferably about 70nanometers thick, while the protective layer 8 ranges between 10 and 30micrometers.

Each of these dimensions, however, is independent of the depth of pits 4and 4′. As is further shown in FIG. 6, a light source 10 is providedbeneath the substantially planar lower surface 6 of the light-readableinformation recording disc 1. In general commercial use today, the lightsource 10 is a laser operating at a wavelength of 780 nanometers in air(in a CD-player) or 650 nanometers in air (in a DVD-player). The type oflight source 10 and its operating wavelength are, however, also mate ofchoice.

In accordance with the present invention, the operating wavelength ofthe fight source λ, the transverse magnification of the optical readerM_(T), the order of interference m, selected from a group consisting ofodd integers, and the refractive index n of the transparent material 5determine the depth d of pits 4 and 4′:

${d = {\frac{\lambda}{2n}\frac{m}{1 + M_{T}^{2}}}},{\left( {{m = 1},3,5,\;\ldots}\mspace{14mu} \right).}$Thus, for λ=780 nm, M_(T)=0.5, m=1, and n=1.55 (the refractive index ofpolycarbonate), the optimum depth of the pits would be about 201nanometers. On the other hand, for λ=650 nm, M_(T)=0.5, m=1, and n=1.55,the optimum pit depth is about 168 nanometers.

Embodiment 2

According to another aspect of the present invention, parameters of theoptical system used to read an information recording medium can beselected so as to maximize the light intensity differences between landsand pits for an already set depth of the pits, such as in a commerciallyavailable CD.

As shown above, for the maximum contrast, the depth of said pits shouldbe equal to about:

${\frac{\lambda}{2n}\frac{m}{1 + M_{T}^{2}}},$where λ is the wavelength of light, used to read the informationrecording medium, m is the order of interference selected from a groupconsisting of odd integers, M_(T) is the transverse magnification of thereader, and n is the refractive index of the material within the pits.

If the depth of the pits of a commercially available CD is about 114nanometers and the refractive index n is 1.55, the optimum systemparameters should satisfy the relationship:353(1+M _(T) ²)=mλ(in nanometers)Choosing λ=780 nm and m=3, the optimum transverse magnification M_(T) ofthe system becomes about 2.37. For the same wavelength at the source, ifm=13, M_(T) becomes about 5.

For a commercially available DVD with the pit depth at about 100 andn=1.55:310(1+M _(T) ²)=mλ(in nanometers)choosing λ=650 nm and m=13, the optimum transverse magnification M_(T)becomes about 5, just as for a commercially available CD. Accordingly,an optic reader with the transverse magnification of 5 can be used toread both commercially available CDs and DVDs.

Embodiment 3

Finally, the present invention also facilitates building acustom-designed system for reading an information recording medium. Forexample, if the system requirements include a longer wavelength laser(e.g., 1064 nm min air), large magnification (e.g., 10), and a pits andlands structure that is exposed to air, the relationship of theremaining parameters is governed by the expression:d(in nanometers)=5.26 nm.It is clear that if d is on the order of several nanometers, themanufacturing of such information recording media will be difficult andcostly. In the absence of additional requirements, m can be madesufficiently large, for example 41. Under these conditions, d becomesabout 216 nanometers.

It will be understood that the foregoing is only illusive of theprinciples of this invention, and that various modifications can be madeby those skilled in the art without departing from the scope and spiritof the invention.

1. An information recording medium readable by an optical readercomprising: transparent substrate having one substantially planarsurface and a second surface opposite said first surface, said secondsurface formed as a data storage structure including pits and lands, inwhich the depth of said pits is equal to about:${\frac{\lambda}{2n}\frac{m}{1 + M_{T}^{2}}},$ wherein λ is a wavelengthof the light used to read the information recording medium, n is arefractive index of the substrate, m is the order of interferenceselected from a group consisting of odd integers, and M_(T) is atransverse magnification of the reader, wherein said pit depth, d, isselected to satisfy the following condition:$\frac{\lambda_{n}}{5.3} \leq d \leq \frac{\lambda_{n}}{4}$ a lightreflecting coating on said second surface for reflecting said lightpassed through said transparent substrate, said coating conforming tothe contours of said second surface so that said light is reflected backthrough the transparent substrate in accordance with the informationrecorded by means of said pits and lands.
 2. The information recordingmedium defined in claim 1, wherein said medium is disc-shaped.
 3. Theinformation recording medium defined in claim 1, wherein saidtransparent substrate is selected from the group consisting ofpolymethyl methacrylate, photo polymer and polycarbonate.
 4. Theinformation recording medium defined in claim 1, wherein saidlight-reflecting coating is selected from the group consisting of gold,silver and aluminum.
 5. An information recording medium readable by anoptical reader comprising: a transparent substrate having onesubstantially planar surface and a second surface opposite to said firstsurface, said second surface formed as a data storage structureincluding pits and lands, in which the depth of said pits is equal toabout: ${\frac{\lambda}{2n}\frac{m}{1 + M_{T}^{2}}},$ wherein λ is awavelength of the light used to read the information recording Medium, nis a refractive index of the substrate, m is the order of interferenceselected from a group consisting of odd integers, and M_(T) is atransverse magnification, wherein said pit depth, d, is selected tosatisfy the following condition:$\frac{\lambda_{n}}{5.3}\underset{\_}{<}d\underset{\_}{<}\frac{\lambda_{n}}{4}$a light-reflecting coating on said second surface for reflecting saidlight passed through said transparent substrate, said coating conformingto the contours of said second surface so that said light is reflectedback through the transparent substrate in accordance with theinformation recorded by means of said pits and lands; and a protectivecoating having a first surface conforming to the contours of saidlight-reflecting coating and a second surface opposite to said firstsurface being substantially planar.
 6. The information recording mediumdefined in claim 5, wherein said medium is disc-shaped.
 7. Theinformation recording medium defined in claim 5, wherein saidtransparent substrate is selected from the group consisting ofpolymethyl methacrylate, photo polymer and polycarbonate.
 8. Theinformation recording medium defined in claim 5, wherein saidlight-reflecting coating is selected from the group consisting of gold,silver and aluminum.
 9. The information recording medium defined inclaim 5, wherein said protective coating is lacquer.